Polyarylene sulfides are generally formed via a reaction of a dihaloaromatic monomer with an alkali metal sulfide in the presence of an organic amide solvent. The reaction often occurs over multiple stages during which a low molecular weight prepolymer is initially formed, and then the molecular weight is increased in a subsequent step. The stages are generally carried out in a batch-wise fashion within a single reactor. Unfortunately, polyarylene sulfides formed from these processes tend to have too low of a melt viscosity for use in certain types of applications. As such, a need currently exists for a method of forming high viscosity polyarylene sulfides.